Higher-order estimation of active and reactive acoustic intensity

et al. 2017

Self Cite

Sound intensity measurements using two microphones have traditionally been processed using a cross-spectral method with inherent error in the finite-sum and finite-difference formulas. The phase and amplitude gradient estimator method (PAGE) has been seen experimentally to extend the bandwidth of broadband active intensity estimates by an order of magnitude. To provide an analytical foundation for the method, bias errors in active intensity and specific acoustic impedance are presented and compared to those of the traditional method. Bias errors are reported for a plane-wave field and sound radiated from a monopole and a dipole. Additionally, bias errors are reported for reactive intensity, the estimation of which is unchanged by the PAGE method for the two-microphone case.

Section: Discussionmentioning

confidence: 99%

Bias error analysis for phase and amplitude gradient estimation of acoustic intensity and specific acoustic impedance

Whiting

Lawrence

et al. 2017

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“…Since the magnitude and angular parts are separable, this scaling factor would have no adverse effects on the calculation of the angle. This correction works perfectly for a plane-wave source with contaminating uncorrelated noise, and may be useful for other source and contaminating noise situations; [13][14][15]17,18 this correction will be explored in connection with a forthcoming coherence-based PAGE calculation method. With or without correction, the PAGE method computes the correct intensity angle for a plane-wave source with uncorrelated noise, regardless of the values for ka, SNR, or angle of incidence.…”

Section: (A)mentioning

confidence: 99%

The effects of contaminating noise on the calculation of active acoustic intensity for pressure gradient methods

Cook

Neilsen

et al. 2019

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Bias errors for two-dimensional active acoustic intensity using multi-microphone probes have been previously calculated for both the traditional cross-spectral and the Phase and Amplitude Gradient Estimator (PAGE) methods [Whiting, Lawrence, Gee, Neilsen, and Sommerfeldt, J. Acoust. Soc. Am. 142, 2208-2218 (2017)]. Here, these calculations are expanded to include errors due to contaminating noise, as well as probe orientation. The noise can either be uncorrelated at each microphone location or self-correlated; the self-correlated noise is modeled as a plane-wave with a varying angle of incidence. The intensity errors in both magnitude and direction are dependent on the signal-to-noise ratio (SNR), frequency, source properties, incidence angles, probe configuration, and processing method. The PAGE method is generally found to give more accurate results, especially in direction; however, uncorrelated noise with a low SNR (below 10-15 dB) and low frequency (wavelengths more than 1/4 the microphone spacing) can yield larger errors in magnitude than the traditional method-though a correction for this is possible. Additionally, contaminating noise does not necessarily impact the possibility of using the PAGE method for broadband signals beyond a probe's spatial Nyquist frequency. V

Three-microphone probe bias errors for acoustic intensity and specific acoustic impedance

Lawrence

Whiting

et al. 2018

In acoustic intensity estimation, adding a microphone at the probe center removes errors associated with pressure averaging. Analytical bias errors are presented for a one-dimensional, three-microphone probe for active intensity, reactive intensity, and specific acoustic impedance in a monopole field. Traditional estimation is compared with the Phase and Amplitude Gradient Estimator (PAGE) method; the PAGE method shows an increased bandwidth for all three quantities. The two- and three-microphone methods are compared experimentally, showing reduced bias errors with three-microphone PAGE for active and reactive intensity, whereas using two microphones is preferred for specific acoustic impedance.